Diaphragm deflection's impact on unreinforced masonry 4

[WARose]

The situation: A portion of a existing floor acting as a diaphragm is supported (vertically only) by 8' tall cantilever, unreinforced masonry columns. The lateral force resisting system is masonry shear walls.

The Problem/Question: My calculations indicate the diaphragm deflection (as well as other displacements) would create more displacement and moment in the columns than is allowed. (This is for wind loading by the way. Seismic is nothing where this is.) Ergo, my question is: what does that mean for the columns? That they will be destroyed and not be able to transfer vertical load during (and after) such a event? I've never been too clear about this on unreinforced masonry.

Notes: As stated, this is for wind loading only. Also, please don't make any alteration suggestions. For right now, I just want to get those questions answered.

Thanks.

 

[r13]

Deflection caused by wind load on floor? How it happened, and what is the nature of the deflection, or it is drift? You need to provide a better description/picture.

 

[bones206]

I think you have to apply the principle of deformation compatibility. In other words, the diaphragm deflection at the top of the column must equal the lateral displacement of the top of the column. Whatever forces/stresses resulting from that are what they are. I think the principle is the same regardless of whether the load is seismic or wind.

 

[phamENG]

WARose - Generally I would say yes. If the diaphragm will deflect more than the columns can accommodate, something's going to fail. What it is and what the consequences are for the building will, of course, vary based on the circumstance. How far has it deflected? Would the diaphragm's tendency to return to its undeflected shape be insufficient to overcome the destabilizing moment created by the now eccentric load from the leaning column?

Hopefully you don't count this as an alteration suggestion, as I think it may help to give you a more realistic handle on the situation: have you attempted running your analysis assuming the columns provide some lateral resistance? Prior to cracking, they will restrain deflection in the diaphragm if properly connected. You could try simulating them as springs: determine the deflection of one column at or just below the lateral load that creates its cracking moment (modulus of rupture in the bed joint) and back out a spring stiffness. Plug that into your analysis and see what the resulting reactions at the columns are. If they are less than the load that produces flexural cracking, then you probably don't have too much to worry about.

EDIT: this does assume you've modeled it in some sort of software. Mixing spring and rigid supports in hand calcs is a bit of a PITA.

 

[WARose]

Deflection caused by wind load on floor?

Yes. Diaphragm deflection from lateral loads.

How it happened, and what is the nature of the deflection, or it is drift?

This is what could happen. Not what has happened. These are (again) displacements due to a design wind load.

 

[WARose]

If the diaphragm will deflect more than the columns can accommodate, something's going to fail.

That's what I am afraid of.

You could try simulating them as springs: determine the deflection of one column at or just below the lateral load that creates its cracking moment (modulus of rupture in the bed joint) and back out a spring stiffness. Plug that into your analysis and see what the resulting reactions at the columns are. If they are less than the load that produces flexural cracking, then you probably don't have too much to worry about.

That's a good idea. What was blowing me out of the water (aside from the deflection) was the the fact I was well in excess of allowable flexural tensile stresses as per the code. I'll have to look up what f_r is as per ACI 530. (Although I don't know if this is a acceptable approach.) Thanks.

 

[bones206]

Modelling it as a spring is essentially applying the principle of deformation compatibility. Makes sense to me.

 

[WARose]

Modelling it as a spring is essentially applying the principle of deformation compatibility.

yep. Although the sketchy part to me is comparing the stresses to the modulus of rupture. IIRC, that stress is typically in excess of the allowable tensile stress in the code. So I will have to think/research more there. (Unreinforced masonry is not something I do much of.)

 

[KootK]

Any chance the diaphragm flexibility has been grossly underestimated? What are we dealing with here for materials, span between shear walls, and diaphragm depth?

Also, what's the nature of the column construction? 16 x 16 pilaster blocks? Or stack of bricks?

 

[WARose]

Any chance the diaphragm flexibility has been grossly underestimated?

I don't think so. I've looked at that several different ways.

What are we dealing with here for materials, span between shear walls, and diaphragm depth?

Not sure I know what materials you want (I may answer it anyway in this reply).....span between walls: about 80'. Diaphragm depth: about 30'

Also, what's the nature of the column construction? 16 x 16 pilaster blocks? Or stack of bricks?

16"x 12" (fully grouted) CMU stacked on top of each other.

 

[r13]

I asked because I must have misunderstand something, since it seems just a matter of masonry design to resist the combined loadings.

 

[KootK]

As for a realistic expectation of behavior, I suspect that you'd develop a mechanism something like that shown below.

 

[KootK]

Not sure I know what materials you want (I may answer it anyway in this reply)

I was wondering about the construction of the diaphragm itself. Timber decking? Your diaphragm aspect ratio is not excessive so I'm guessing that you're dealing with diaphragm panels that are shear flexible.

 

[WARose]

As for a realistic expectation of behavior, I suspect that you'd develop a mechanism something like that shown below.

Thanks Kootk. That's something like I was visualizing. If you will recall, you and I got in a discussion some time back about something similar:

https://www.eng-tips.com/viewthread.cfm?qid=451554

Along those lines, I was wondering how much it can move without destroying it.

I was wondering about the construction of the diaphragm itself. Timber decking?

Yes.

 

[KootK]

My intent with my previous sketch was to suggest a limit to how much it can move safely (URM safely at least). Maybe thickness /3?

I will say, however, that I find the combination of a timber deck diaphragm with URM columns pretty unnerving just as a matter of principle. Any chance you could sheath over the decking to stiffen it up?

That document that Agent666 posted in your timber decking diaphragm thread must be pretty relevant to what you're doing. Nothing in there for guidance?

 

[WARose]

I will say, however, that I find the combination of a timber deck diaphragm with URM columns pretty unnerving just as a matter of principle.

Me too.

Any chance you could sheath over the decking to stiffen it up?

Now what did I say about alteration suggestions? (Just kidding. )

But seriously, I'm not sure how much a 3/8" cover on 1.5" boards would help. But it is something I am thinking about.

That document that Agent666 posted in your timber decking diaphragm thread must be pretty relevant to what you're doing. Nothing in there for guidance?

Nothing I've seen so far. But still am looking. I figured this to be a fundamental unreinforced masonry question. (Which I (again) don't do much of.)

 

[bones206]

Did you include the effect of gravity loads in the masonry column net tensile stress calc? That would help.

 

[WARose]

Did you include the effect of gravity loads in the masonry column net tensile stress calc? That would help.

Yep. It helped.....but not enough.

 

[KootK]

Now what did I say about alteration suggestions?

Doh, I'm such a bad listener.

But seriously, I'm not sure how much a 3/8" cover on 1.5" boards would help.

I would expect lots, both in terms of actual performance and your ability to justify performance. Ditch that BS, nailed moment connection stuff.

It doesn't take a whole lot of movement to crack a URM anything. As such, if we're unwilling to consider models that include cracking, I would think that we'd have to scrap a good chunk of infrastructure. Even with a better diaphragm, I think that you'd struggle to dial the movement down low enough to not crack URM in flexure.

 

[WARose]

I would expect lots, both in terms of actual performance and your ability to justify performance. Ditch that BS, nailed moment connection stuff.

Yeah....I'm still looking at it.

It doesn't take a whole lot of movement to crack a URM anything. As such, if we're unwilling to consider models that include cracking, I would think that we'd have to scrap a good chunk of infrastructure. Even with a better diaphragm, I think that you'd struggle to dial the movement down low enough to not crack URM in flexure.

Yep. I have to say though: thinking about it in terms of allowable seismic drift.....why wouldn't it work (at least in terms of deflection)? (Even though this isn't seismic.)

Of course....considering how unreinforced masonry does in earthquakes....